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Long strange segments in a long-range-dependent moving average

Author

Listed:
  • T. Rachev, Svetlozar
  • Samorodnitsky, Gennady

Abstract

We establish the rate of growth of the length of long strange intervals in an infinite moving average process whose coefficients are regularly varying at infinity. We compute the limiting distribution of the appropriately normalized length of such intervals. The rate of growth of the length of long strange intervals turns out to change dramatically once the exponent of regular variation of the coefficients becomes smaller than 1, and then the rate of growth is determined both by the exponent of regular variation of the coefficients and by the heaviness of the tail distribution of the noise variables.

Suggested Citation

  • T. Rachev, Svetlozar & Samorodnitsky, Gennady, 2001. "Long strange segments in a long-range-dependent moving average," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 119-148, May.
    • Handle: RePEc:eee:spapps:v:93:y:2001:i:1:p:119-148
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    Citations

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    Cited by:

    1. Sun, Wei & Rachev, Svetlozar & Fabozzi, Frank J., 2007. "Fractals or I.I.D.: Evidence of long-range dependence and heavy tailedness from modeling German equity market returns," Journal of Economics and Business, Elsevier, vol. 59(6), pages 575-595.
    2. Wei Sun & Svetlozar Rachev & Frank Fabozzi & Petko Kalev, 2008. "Fractals in trade duration: capturing long-range dependence and heavy tailedness in modeling trade duration," Annals of Finance, Springer, vol. 4(2), pages 217-241, March.
    3. McElroy, Tucker & Jach, Agnieszka, 2012. "Tail index estimation in the presence of long-memory dynamics," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 266-282.
    4. Ghosh, Souvik & Samorodnitsky, Gennady, 2010. "Long strange segments, ruin probabilities and the effect of memory on moving average processes," Stochastic Processes and their Applications, Elsevier, vol. 120(12), pages 2302-2330, December.
    5. Fasen, Vicky & Roy, Parthanil, 2016. "Stable random fields, point processes and large deviations," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 832-856.
    6. Wei Sun & Svetlozar Rachev & Frank J. Fabozzi, 2009. "A New Approach for Using Lévy Processes for Determining High‐Frequency Value‐at‐Risk Predictions," European Financial Management, European Financial Management Association, vol. 15(2), pages 340-361, March.
    7. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    8. Wei Sun & Svetlozar Rachev & Frank Fabozzi & Petko Kalev, 2009. "A new approach to modeling co-movement of international equity markets: evidence of unconditional copula-based simulation of tail dependence," Empirical Economics, Springer, vol. 36(1), pages 201-229, February.
    9. Sun Wei & Rachev Svetlozar & Stoyanov Stoyan V. & Fabozzi Frank J., 2008. "Multivariate Skewed Student's t Copula in the Analysis of Nonlinear and Asymmetric Dependence in the German Equity Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-37, May.

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